Example #1
0
def freq_pdf_old(x, p, n, t, k=8):

    if x > 0.5:
        return freq_pdf2(1.0-x, 1.0-p, n, t, k)
    
    q = 1.0 - p
    prob = -util.INF
    sgn = 1
    t4n = t / (4*n)
    
    for i in xrange(1, k+1):
        #term = (p * q * i * (i+1) * (2*i+1) *
        #        hypergeo(1-i,i+2,2,p) * hypergeo(1-i,i+2,2,x) *
        #        exp(-t * i * (i+1) / (4*n)))

        lcoff = log(p * q * i * (i+1) * (2*i+1))
        h1 = hypergeo(1-i,i+2,2,p, i+2)
        h2 = hypergeo(1-i,i+2,2,x, i+2)
        sgn2 = util.sign(h1) * util.sign(h2)

        if sgn2 != 0:
            term = (lcoff + log(abs(h1)) + log(abs(h2)) +
                    (- i * (i+1) * t4n))
            sgn, prob = stats.logadd_sign(sgn, prob, sgn2, term)

    return sgn * exp(prob)
Example #2
0
def hypergeo(a, b, c, z, k=100):
    """Hypergeometric function"""
    terms = [0.0]
    signs = [1.0]
    for i in xrange(1, k+1):
        term = float((i+a-1)*(i+b-1)*z)/(i+c-1)/i
        signs.append(util.sign(term) * signs[-1])
        if term == 0.0:
            break
        terms.append(log(abs(term)) + terms[i-1])
    return sum(s*exp(i) for s, i in zip(signs, terms))
Example #3
0
def loghypergeo(a, b, c, z, k=100):
    """
    Hypergeometric function

    Performs computation in log-space
    """
    terms = [0.0]
    signs = [1.0]
    for i in xrange(1, k+1):
        term = float((i+a-1)*(i+b-1)*z)/(i+c-1)/i
        signs.append(util.sign(term) * signs[-1])
        if term == 0.0:
            break
        terms.append(log(abs(term)) + terms[i-1])

    sgn = 1
    tot = -util.INF

    for s, t in zip(signs, terms):
        sgn, tot = stats.logadd_sign(sgn, tot, s, t)
    return sgn, tot